When I run the program inaccurate results appear What is the problem?

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sadeem alqarni
sadeem alqarni on 16 Feb 2019
Commented: Star Strider on 25 Feb 2019
syms t y1 y2 y3 y4 yn11 yn1 yr yr11 yr111 yr v y(v) x
format longe
h=0.1
r=1.7686999343761197980595002942562 %1694/911=1.859495060373216e+00
x=0
y0=0
y01=0.25;
y011=0;
fn=-y01+y0.*y01.*y011
fnr=-yr11+yr.*yr11.*yr111
fn1=-yn1+y1.*yn1.*yn11
fn2=-y3+y2.*y3.*y4
eq1 =-y2-(r - 2)/r*y0+ 2/(r*(r - 1))*yr+ (2*r - 4)/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 23*r + 6))/(120*r)*fn+ (h.^3.*(- r^2 + 2*r + 3))/(60*r)*fnr -(h.^3.*(- r^3 + 4*r^2 + 9*r - 26))/60*fn1+ (h.^3.*(- r^3 + 2*r + 1))/120*fn2
eq2= -h.*y3 -(r - 3)/r*y0+ 3/(r*(r - 1))*yr+ (r - 4)/(r - 1)*y1 -(h.^3.*(3*r^4 - 24*r^3 + 66*r^2 - 67*r + 12))/(240*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r - 4))/(40*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- 3*r^4 + 15*r^3 + 15*r^2 - 137*r + 116))/(120*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 3*r - 12))/(80*(r - 2))*fn2
eq3=-h.^2.*y4+2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1+ (h.^3.*(- r^4 + 8*r^3 - 22*r^2 + 18*r + 5))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 - 75*r + 77))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 42*r - 81))/(120*(r - 2))*fn2
eq4=-h.*yn1 -(r - 1)/r*y0+ 1/(r*(r - 1))*yr+ (r - 2)/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 21*r + 6))/(240*r)*fn+ (h.^3.*(- r^2 + 2*r + 3))/(120*r)*fnr -(h.^3.*(- r^3 + 4*r^2 + 9*r - 8))/120*fn1 -(h.^3.*(r^3 - 2*r + 1))/240*fn2
eq5=-h.^2.*yn11+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 28*r + 10))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r - 10))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 - 35*r + 22))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 - 8*r + 4))/(120*(r - 2))*fn2
eq6=-h.*yr11+ (r - 1)/r*y0+ (2*r - 1)/(r*(r - 1))*yr -r/(r - 1)*y1+ (h.^3.*(2*r^4 - 13*r^3 + 28*r^2 - 22*r + 5))/240*fn+ (h.^3.*(4*r^3 - 15*r^2 + 10*r + 5))/(120*(r - 2))*fnr+ (h.^3.*r*(- 2*r^3 + 7*r^2 + 2*r - 3))/120*fn1+ (h.^3.*r*(2*r^4 - 5*r^3 + 2*r^2 + 2*r - 1))/(240*(r - 2))*fn2
eq7=-h.^2.*yr111+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1+ (h.^3.*(4*r^4 - 22*r^3 + 38*r^2 - 22*r + 5))/(120*r)*fn -(h.^3.*(- 14*r^4 + 55*r^3 - 55*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(4*r^4 - 15*r^3 + 5*r^2 + 5*r - 3))/(60*(r - 1))*fn1+ (h.^3.*(4*r^4 - 8*r^3 + 2*r^2 + 2*r - 1))/(120*(r - 2))*fn2
eq8=-h.*y01 -(r + 1)/r*y0 -1/(r*(r - 1))*yr+ r/(r - 1)*y1+ (h.^3.*(r^3 - 8*r^2 + 22*r - 5))/240*fn+ (h.^3.*(r^3 - 5*r^2 + 5*r + 5))/(120*(r^2 - 3*r + 2))*fnr+ (h.^3.*r*(- r^3 + 5*r^2 + 5*r - 3))/(120*(r - 1))*fn1 -(h.^3.*r*(- r^3 + 2*r^2 + 2*r - 1))/(240*(r - 2))*fn2
eq9 =-h.^2.*y011+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 + 22*r - 5))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 + 5*r - 3))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 2*r - 1))/(120*(r - 2))*fn2
[y1,y2,y3,y4,yn1,yn11,yr,yr11,yr111]=vpasolve([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9])

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Accepted Answer

Star Strider
Star Strider on 16 Feb 2019
The best approach to this is likely not the vpasolve function, since it takes forever.
I have no idea of these are the ‘accurate’ results you want (I have no idea what that means), however you will get them much more quickly:
syms t y1 y2 y3 y4 yn11 yn1 yr yr11 yr111 yr v y(v) x
format longe
h=0.1;
r=1.7686999343761197980595002942562; %1694/911=1.859495060373216e+00
x=0;
y0=0;
y01=0.25;
y011=0;
fn=-y01+y0.*y01.*y011;
fnr=-yr11+yr.*yr11.*yr111;
fn1=-yn1+y1.*yn1.*yn11;
fn2=-y3+y2.*y3.*y4;
eq1 =-y2-(r - 2)/r*y0+ 2/(r*(r - 1))*yr+ (2*r - 4)/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 23*r + 6))/(120*r)*fn+ (h.^3.*(- r^2 + 2*r + 3))/(60*r)*fnr -(h.^3.*(- r^3 + 4*r^2 + 9*r - 26))/60*fn1+ (h.^3.*(- r^3 + 2*r + 1))/120*fn2;
eq1 = simplifyFraction(eq1);
eq1d = vpa(eq1, 5)
eq2= -h.*y3 -(r - 3)/r*y0+ 3/(r*(r - 1))*yr+ (r - 4)/(r - 1)*y1 -(h.^3.*(3*r^4 - 24*r^3 + 66*r^2 - 67*r + 12))/(240*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r - 4))/(40*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- 3*r^4 + 15*r^3 + 15*r^2 - 137*r + 116))/(120*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 3*r - 12))/(80*(r - 2))*fn2;
eq2 = simplifyFraction(eq2);
eq2d = vpa(eq2, 5)
eq3=-h.^2.*y4+2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1+ (h.^3.*(- r^4 + 8*r^3 - 22*r^2 + 18*r + 5))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 - 75*r + 77))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 42*r - 81))/(120*(r - 2))*fn2;
eq3 = simplifyFraction(eq3);
eq3d = vpa(eq3, 5)
eq4=-h.*yn1 -(r - 1)/r*y0+ 1/(r*(r - 1))*yr+ (r - 2)/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 21*r + 6))/(240*r)*fn+ (h.^3.*(- r^2 + 2*r + 3))/(120*r)*fnr -(h.^3.*(- r^3 + 4*r^2 + 9*r - 8))/120*fn1 -(h.^3.*(r^3 - 2*r + 1))/240*fn2;
eq4 = simplifyFraction(eq4);
eq4d = vpa(eq4, 5)
eq5=-h.^2.*yn11+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 - 28*r + 10))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r - 10))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 - 35*r + 22))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 - 8*r + 4))/(120*(r - 2))*fn2;
eq5 = simplifyFraction(eq5);
eq5d = vpa(eq5, 5)
eq6=-h.*yr11+ (r - 1)/r*y0+ (2*r - 1)/(r*(r - 1))*yr -r/(r - 1)*y1+ (h.^3.*(2*r^4 - 13*r^3 + 28*r^2 - 22*r + 5))/240*fn+ (h.^3.*(4*r^3 - 15*r^2 + 10*r + 5))/(120*(r - 2))*fnr+ (h.^3.*r*(- 2*r^3 + 7*r^2 + 2*r - 3))/120*fn1+ (h.^3.*r*(2*r^4 - 5*r^3 + 2*r^2 + 2*r - 1))/(240*(r - 2))*fn2;
eq6 = simplifyFraction(eq6);
eq6d = vpa(eq6, 5)
eq7=-h.^2.*yr111+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1+ (h.^3.*(4*r^4 - 22*r^3 + 38*r^2 - 22*r + 5))/(120*r)*fn -(h.^3.*(- 14*r^4 + 55*r^3 - 55*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(4*r^4 - 15*r^3 + 5*r^2 + 5*r - 3))/(60*(r - 1))*fn1+ (h.^3.*(4*r^4 - 8*r^3 + 2*r^2 + 2*r - 1))/(120*(r - 2))*fn2;
eq7 = simplifyFraction(eq7);
eq7d = vpa(eq7, 5)
eq8=-h.*y01 -(r + 1)/r*y0 -1/(r*(r - 1))*yr+ r/(r - 1)*y1+ (h.^3.*(r^3 - 8*r^2 + 22*r - 5))/240*fn+ (h.^3.*(r^3 - 5*r^2 + 5*r + 5))/(120*(r^2 - 3*r + 2))*fnr+ (h.^3.*r*(- r^3 + 5*r^2 + 5*r - 3))/(120*(r - 1))*fn1 -(h.^3.*r*(- r^3 + 2*r^2 + 2*r - 1))/(240*(r - 2))*fn2;
eq8 = simplifyFraction(eq8);
eq8d = vpa(eq8, 5)
eq9 =-h.^2.*y011+ 2/r*y0+ 2/(r*(r - 1))*yr -2/(r - 1)*y1 -(h.^3.*(r^4 - 8*r^3 + 22*r^2 + 22*r - 5))/(120*r)*fn -(h.^3.*(r^4 - 5*r^3 + 5*r^2 + 5*r + 5))/(60*r*(r^2 - 3*r + 2))*fnr -(h.^3.*(- r^4 + 5*r^3 + 5*r^2 + 5*r - 3))/(60*(r - 1))*fn1+ (h.^3.*(- r^4 + 2*r^3 + 2*r^2 + 2*r - 1))/(120*(r - 2))*fn2;
eq9 = simplifyFraction(eq9);
eq9d = vpa(eq9, 5)
eqsfcn = matlabFunction([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9], 'Vars',{[y1,y2,y3,y4,yn1,yn11,yr,yr11,yr111]})
eqsol = fsolve(eqsfcn, rand(1,9))
eqsolc = num2cell(eqsol);
[y1,y2,y3,y4,yn1,yn11,yr,yr11,yr111] = eqsolc{:}
I used the simplifyFraction function to do just that with your equations, then the fsolve function to do the actual calculations. These changes make it significantly more efficient.
The results I got are:
y1 =
2.495835158216658e-02
y2 =
4.966725033036157e-02
y3 =
2.450145921764798e-01
y4 =
-4.970810349993776e-02
yn1 =
2.487509121241510e-01
yn11 =
-2.496352514349295e-02
yr =
4.398727143758653e-02
yr11 =
2.460985502335340e-01
yr111 =
-4.401564490668385e-02
You must be certain your equations are written as you want them to be in order to get ‘accurate’ values. We have no control over that.
Experiment to get the results you want.
  2 Comments
sadeem alqarni
sadeem alqarni on 25 Feb 2019
i want the values of y1(0.1) ,y2(0.1),y3(0.1),y4(0.1),yn1(0.1), yn11(0.1), yr(0.1), yr11(0.1),yr111(0.1)how can I get it?
Star Strider
Star Strider on 25 Feb 2019
I do not undetrstand what you are asking.
Those values are conatants, not functions. Your code solves for them as constants.

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